On orthogonal polynomials and related discrete integrable systems [PDF]
, 2006 Orthogonal polynomials arise in many areas of mathematics and have been the subject of interest by many mathematicians. In recent years this interest has often arisen from outside the orthogonal polynomial community after their connection with ...
Spicer, Paul Edward
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On tau functions for orthogonal polynomials and matrix models. [PDF]
, 2011 Let v be a real polynomial of even degree, and let \rho be the equilibrium probability measure for v with support S; to that v(x) greeater than or equal to \int 2log |x-y| \rho (dy) +C for some constant C with equality on S.
Blower, Gordon
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Spectral method of electrical circuits accelerated simulation with thyristors
Elektrotehnìka ta Elektroenergetika, 2023 Purpose. The development of transient processes calculation method in electric circuits with thyristors based on the use of functions approximation by orthogonal polynomials. Methodology.
S.M. Tykhovod +3 more
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Computation of Fourier transform representations involving the generalized Bessel matrix polynomials
Advances in Difference Equations, 2021 Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of ...
M. Abdalla, M. Akel
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On some hypergeometric Sobolev orthogonal polynomials with several continuous parameters
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2023 In this paper we study the following hypergeometric polynomials: $$ \mathcal{P}_n(x) = \mathcal{P}_n(x;\alpha,\beta,\delta_1, \dots,\delta_\rho,\kappa_1,\dots,\kappa_\rho) = $$ $$ = {}_{\rho+2} F_{\rho+1} (-n,n+\alpha+\beta+1,\delta_1+1, \dots,\delta_ ...
Sergey Zagorodnyuk
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Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure [PDF]
, 2016 This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure for x in [0,?), ?
Deaño Cabrera, Alfredo +6 more
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Special values of L-functions for orthogonal groups
Comptes Rendus. Mathématique, 2017 This is an announcement of certain rationality results for the critical values of the degree-2 n L -functions attached to GL
Bhagwat, Chandrasheel, Raghuram, A.
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Monopole harmonics on $\mathbb{CP}^{n-1}$
SciPost Physics, 2023 We find the spectra and eigenfunctions of both ordinary and supersymmetric quantum-mechanical models describing the motion of a charged particle over the $\mathbb{CP}^{n-1}$ manifold in the presence of a background monopole-like gauge field.
Dmitri Bykov, Andrei Smilga
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The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation [PDF]
, 2013 We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations
Clarkson, Peter +3 more
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Bernstein spectral method for quasinormal modes and other eigenvalue problems
European Physical Journal C: Particles and Fields, 2023 Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes.
Sean Fortuna, Ian Vega
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